I'm hangin' on a hangover

The hangover for Ye is the lingering pain of the end of his relationship with Alexis Phifer five years ago. She was his intoxication, and now Ye is dealing with the headaches and feverish desire of an alcoholic because of her.

Ye also plays with the words hanging and hangover. The word ‘hanging’ means to be suffering from a hangover and works well in this sentence, as well as the imagery evoking a picture of Kanye literally hanging onto the hangover which is killing him.